Examples for Cross Curvature Flow on 3-Manifolds

Details Examples for Cross Curvature Flow on 3-Manifolds Examples for Cross Curvature Flow on 3-Manifolds

2004-05-14

arxiv.org/abs/math/0405275v1

Mathematics

Differential Geometry

14 pages

Scientific paper

Recently, B.Chow and R.S.Hamilton introduced the cross curvature flow on 3-manifolds. In this paper, we analyze two interesting examples for this new flow. One is on a square torus bundle over a circle, and the other is on a $S^{2}$ bundle over a circle. We show that the global flow exist in both cases. But on the former the flow diverges at time infinity, and on the latter the flow converges at time infinity.

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